A tempered subdiffusive Black-Scholes model

TL;DR

This paper introduces a numerical finite difference method for the tempered subdiffusive Black-Scholes model, deriving the governing fractional differential equation and analyzing the method's stability, convergence, and accuracy.

Contribution

It develops a $2- ext{alpha}$ order accurate finite difference scheme for option pricing in the tempered subdiffusive Black-Scholes model, including stability and convergence analysis.

Findings

The method achieves $2- ext{alpha}$ order accuracy in time.

Numerical results validate the stability and convergence of the scheme.

The approach effectively models subdiffusive dynamics in option pricing.

Abstract

In this paper, we focus on the tempered subdiffusive Black-Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has the $2-\alpha$ order of accuracy with respect to time, where $\alpha\in(0,1)$ is the subdiffusion parameter, and $2$ with respect to space. Furthermore, we provide the stability and convergence analysis. Finally, we present some numerical results.